Essays by Stan Tenen

Some Notes on the Logarithmic and Golden Mean Spirals: Addendum
©1997 Stan Tenen

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A short technical note:

My original copyright vortex sculptures are not, and cannot be, golden spirals, and neither are the illicit copies of my vortex sculptures published by the person referred to in the "Plagiarism Notice" at the top of this website.

  1. The golden spiral is anachronistic. It was not known in the ancient world, and was only algebraically defined by Descartes in modern times. Any scholar attempting to reconstruct what was known thousands of years ago would be taken to be a fool for imposing the golden spiral on work of that period. This imposition has hurt Meru Foundation's credibility, because of the plagiarist's false claims.
  2. The golden spiral is a 2-dimensional form that like all log spirals always increases, and has an infinite number of turns. My original copyright sculpture is a limited, 1-1/2 turn, 3-dimensional form, with the outer turns bent back. As any sane person knows, a circle is not a circle if you cut off part of the arc, or bend it over the edge of a table. The plagiarist could have started with any spiral, even the golden spiral, but once he cut it short and bent it (as he did to match my sculpture), it is no longer the spiral it started as. It's not the same mathematical object -- in fact, it's not even a mathematical object at all.
  3. The plagiarist's nomination of the golden spiral is utterly inconsistent with the other work he took from me. There is no previous example of the symmetry/asymmetry model that I laid out in my paper, The Light in the Meeting Tent, found elsewhere on our website. There is no previous example of any "flame letter" that takes the form of the sculpture I designed. The plagiarist's claims regarding the tetrahedron-and-vortex as models of symmetry and asymmetry are copies of my claims -- and they are entirely inconsistent with his claim that the golden spiral represents the asymmetrical part of the symmetry/asymmetry pair. This is because, as the plagiarist correctly states, the golden spiral is always and entirely self-similar. Although the plagiarist may not wish to know it, self-similarity is the definition of symmetry. That's what the word symmetry means. Thus, on his own (stolen) terms, the plagiarist's claim is mathematically incompetent. The actual spiral vortex that the plagiarist shows, which he copied from me, is the antithesis (opposite) of the golden spiral. It is, in fact, the most symmetrical spiral, not the most asymmetrical spiral.

These false technical claims may sell to the plagiarist's mathematically untrained audiences, but at the same time, they are a technical defamation of my work, which makes it a laughing stock among persons who know the geometry and mathematics.

  1. The golden spiral, being self-similar, always circles itself and mirrors itself, in its own image. If you check your classics, you will find that this matches the description of Narcissus. Narcissus worships himself in his reflection (self-similarity), in his own image. It is ironic indeed that the plagiarist should be so attracted to the symbol of self-love, the golden spiral. (I am not referring to the golden proportion, which is of enormous and proper significance. I am only referring to the golden spiral.)

Further, the Western, Abrahamic faiths -- Judaism, Christianity, and Islam -- are based on the idea of a One God, and on the utter refutation of idolatry. It is absurd for the plagiarist to propose that the ancient western sacred alphabets are based on a golden spiral, because that, in fact, would make them the most horrendous of idols to the persons who used these alphabets. Again, his incompetence makes my work look foolish among experts who know. The golden spiral is not only technically unsound, is not only anachronistic, but it is also directly philosophically opposed to the beliefs of the persons whom the plagiarist claims made use of it. It is, in fact, the archetype of narcissism and idolatry. I can provide numerous academic and mathematical references that discuss the foolishness of the persistence of cult-like belief in the resurrective powers of the golden spiral. The plagiarist's linkage of the golden spiral with immortality is also, like the rest of what he presents, taken from others, and represented as his own. The history of the use of the golden spiral to seduce persons into believing that they can be immortal is well-documented.

    Stan Tenen
    September, 1997